We have only two languages in the system: Japanese and English and I personally think that Drop Down List is irrelevant for this type of input, while radio buttons might be easier.
What do you think?
I would recommend going for Radio buttons since you just have two items to show and using radio buttons you can show the information up front Instead of having the user click on the dropdown list and then select a language.
To quote what this article on dropdown lists says on when to use to dropdown lists
If there’s anywhere between 7 and 15 options, a drop-down list is usually a really good fit. You can put a healthy amount of information in your form without cluttering the entire page, because the list’s options are hidden when you don’t need them.
However, many sites are using drop-down lists with too many options (more than 15) or too few (less than 7), resulting in a poor user experience.
Similarly, when not to use dropdown lists
When drop-down lists have less than 7 options they suffer from a lack of up-front information. The user has to click in order to see the available options.
In these cases you are better off using radio buttons so your users immediately can scan how many options they have and what each of those options are, without clicking anything to reveal this information.
Depends on what does your activity do. Will any bilingual users prefer to select both Japanese and English?
If the answer is yes, your should use listbox or checkboxes.
If no, then go for segmented buttons IMHO Segmented buttons looks better because it's easier to see what is selected vs checkboxs, when selection indicator is just tiny black dot. You may consider using ISO language notation or flags.
Consider Cycle button as well.
if you have total freedom from traditional interface elements then a switch or a dial could work if designed right.
For example; since this is only two states any click within the element region changes it to the other choice. The graphics have to be convincing to pull this off but the benefit is that the user doesn't have to precisely position the mouse cursor over something like a radio button (browser element).
You could also consider creating mutually exclusive buttons that resemble keyboard keys. "JP" is just included as an example, there might be more appropriate text.
Actually, here, it's pretty easy to recognize programatically, wether the input was Japanese or English... it doesn't need more than about 2 lines of code to differentiate between ASCII and Kanji (or Hiragana or Katakana).
Let the computer do it for the user, it doesn't take human intelligence.